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Subset Hypotheses Testing and Instrument Exclusion in the Linear Iv Regression
journal contribution
posted on 2023-05-19, 08:48 authored by Doko Tchatoka, Shis paper explores the sensitivity of plug-in subset tests to instrument exclusion in structural models. Identification-robust statistics based on the plug-in principle have been developed for testing hypotheses specified on subsets of the structural parameters. However, their robustness to instrument exclusion has not been investigated. This paper proposes an analysis of the asymptotic distributions of the limited information maximum likelihood (LIML) estimator and plug-in statistics when potential instruments are omitted. Our results provide several new insights and extensions of earlier studies. We show that the exclusion of instruments can eliminate the first-stage, thus weakening identification and invalidating the plug-in subset inference. However, when instrument omission does not affect LIML consistency, it preserves the plug-in subset test validity, although LIML is no longer asymptotically efficient. Unlike the instrumental variable (IV) estimator, the LIML estimator of the identified linear combination of the nuisance parameter is not asymptotically a Gaussian mixture, even without instrument exclusion.
History
Publication title
Econometric TheoryVolume
31Issue
6Pagination
1192-1228ISSN
0266-4666Department/School
College Office - College of Business and EconomicsPublisher
Cambridge Univ PressPlace of publication
40 West 20Th St, New York, USA, Ny, 10011-4211Rights statement
Copyright 2014 Cambridge University PressRepository Status
- Restricted